7.8: Insulation and Home Heating Fuels (IV)
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Energy Cost
It is clear now that when a unit of fuel is burned not all of it is available to the end user, and that as the furnace efficiency increases, higher amounts of heat will be available. An important question that needs to be addressed is how much it costs to buy the energy or heat to heat a place.
Fuel is usually sold in gallons or CCF or kWh. Comparing the actual cost of energy to produce a certain amount of heat for the end user would be easy if the comparison is made on an energy basis rather than on a unit basis. That is, \$/BTUs rather than \$/gal or CCF or kWh.
To calculate the actual energy cost, use the formula
\[ Actual \, Energy \, Cost = \dfrac{Fuel \, Cost (\tfrac{\$}{Unit \, of \, Fuel})}{Heating \, Value \, (\tfrac{MMBTUs}{Unit \, of \, Fuel}) × Efficiency} \]
Example Problems
Example 1
Let’s say we need one million BTUs to keep a place warm at a certain temperature. What would it cost to get those million BTUs from oil or gas or electricity? Let’s assume that:
Cost, efficiency, and heating value of different materials
| Material | Cost per unit | Efficiency | Heating value |
|---|---|---|---|
| Natural gas | $6.60 per MCF | 0.90 | 1,000,000 BTUs (1 MMBTU) per MCF |
| Oil | $1.25 per gallon | 0.85 | 140,000 BTUs (0.14 MMBTUs) per gallon |
| Electricity | $0.082 per kWh | 0.97 | 3,412 BTUs (0.003412 MMBTUs) per kWh |
- Answer
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Use equation 7.9.1 to calculate the actual energy costs for each material.
For natural gas,
\[ Gas \, Cost = \dfrac{\tfrac{\$6.60}{MCF}}{\tfrac{1 \, MMBTU}{MCF} * 0.90} = \$7.33 \, per \, MMBTU \nonumber\]
For oil in a central heating system,
\[ Oil \, Cost = \dfrac{\tfrac{\$1.25}{gallon}}{\tfrac{0.14 \, MMBTUs}{gallon} * 0.85} = \$10.50 \, per \, MMBTU \nonumber\]
For electricity,
\[ Electrical \, Resistance \, Cost = \dfrac{\tfrac{\$0.082}{kWh}}{\tfrac{0.003412 MMBTUs}{kWh} * 0.97} = \$24.77 \, per \, MMBTU \nonumber\]
Example 2
Your old oil furnace runs at about 68% efficiency. If you buy your oil for $1.02/gal, calculate your actual cost on an MMBTU basis.
- Answer
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The following video goes over the solution.
Example 3
Natural gas costs $9.74/MCF. Heating oil costs 0.99 cents/gal. The natural gas furnace runs at 90% efficiency and the oil furnace runs at 80% efficiency. Which fuel is cheaper?
- Answer
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The following video goes over the solution.
Annual Heating Costs
Example Problems
Example 1
A house in International Falls, MN (HDD = 10,500) consists of 1248 ft2 of walls with an R-value of 13 and 1150 ft2 of roof with an R value of 29. The home is heated with natural gas. The AFUE is 0.90 and the price of natural gas is $0.88/CCF. What is the annual heating cost?
- Answer
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Using equation 7.9.1,
\[ Actual \, Energy \, Cost = \dfrac{\tfrac{\$0.88}{CCF}}{\tfrac{0.1 \, MMBTUs}{CCF} * 0.90} = \$9.80/MMBTU \nonumber\]
Heat required can be calculated from the heat loss. Heat loss from the house is from two sources: walls and the roof. Heat loss from each of these sources for a year (season) can be calculated by using the following equations.
\[ Heat \, Loss \, from \, Walls = \dfrac{1248 ft^2 * 10500°F}{\tfrac{13 ft^2 °Fh}{BTUs}} * 24 \dfrac{h}{day} * 1 \, day = 24.19 \, MMBTUs \nonumber\]
\[ Heat \, Loss \, from \, Roof = \dfrac{1150 ft^2 * 10500°F}{\tfrac{29 ft^2 °Fh}{BTUs}} * 24 \dfrac{h}{day} * 1 \, day = 9.99 \, MMBTUs \nonumber\]
Thus, the annual heat cost can be determined using the following equations.
\[ Total \, Heat \, Loss = 24.19 + 9.99 = 34.18 MMBTUs \nonumber\]
\[ Annual \, Heat \, Cost = 34.18 MMBTUs * \dfrac{\$9.80}{MMBTU} = \$334.96 \nonumber\]
Example 2
A house in Bismark, ND (HDD = 9,000) has 860 ft2 of windows (R = 1), 2,920 ft2 of walls (R = 19), and 3,850 ft2 of roof (R = 22). Calculate how much heating oil is required to heat this house for the heating season. The furnace efficiency is 80%.
- Answer
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The following video covers the solution.